Definition of Probability Terms - Basic Level

Definition of Probability Terms - Basic Level

Dear Readers,

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one. Probability has been introduced in Maths to predict how likely events are to happen. The meaning of probability is basically the extent to which something is likely to happen. This is the basic probability theory, which is also used in the probability distribution, where you will learn the possibility of outcomes for a random experiment. To find the probability of a single event to occur, first, we should know the total number of possible outcomes. .

Q1. Two coins are tossed. Let A be the event that the first coin shows head and B be the event that the second coin shows a tail. Two events A and B are :

•  Mutually exclusive
•  Dependent
•  Independent and mutually exclusive
•  None of these

Solution
None of These

Q2.A card is drawn from a pack of 52 cards. If A = card is of diamond, B = card is an ace and A ∩ B = card is ace of diamond, then events A and B are

•  Independent
•  Mutually exclusive
•  Dependent
•  Equally likely

Solution
A card is drawn from a pack of 52 cards. If A = card is of diamond, B = card is an ace and A ∩ B = card is ace of diamond, then events A and B are Dependent

Q3.  The probabilities of three mutually exclusive events are 2/3, 1/4 and 1/6. The statement is :

•   True
•  False
•  Could be either
•  Do not know

Solution
The probabilities of three mutually exclusive events are 2/3, 1/4 and 1/6. The statement is False

Q4. If P(A₁ ∪ A₂) = 1- P(A₁^c) P(A₂^c), where c stands for complement, then the events A₁ and A₂ are :

•  Mutually exclusive
•  Independent
•  Equally likely
•  None of these

Solution
If P(A₁ ∪ A₂) = 1- P(A₁^c) P(A₂^c), where c stands for complement, then the events A₁ and A₂ are independent

Q5.If ^{(1 - 3p)}⁄₂ , ^{(1 + 4p)}⁄₃ and ^{(1 + p)}⁄₆ are the probabilities of three mutually exclusive and exhaustive events, then the set of all values of p is :

•  [0,1]
•  [^-1⁄₄ , ¹⁄₃]
•  [0,¹⁄₃]
•  [0,∞]

Solution
 The set of all values of p is  [^-1⁄₄ , ¹⁄₃]

Q6. The event A is independent of itself if and only if P(A) =

•  0
•  1
• 0,1
•  None of these

Solution
The event A is independent of itself if and only if P(A) = 0,1

Q7.If A and B are independent events and P(C) = 0, then

•  A and C are independent
•  B and C are independent
•  A, B and C are independent
•  All of these

Solution
If A and B are independent events and P(C) = 0, then all the above conditions holds true

Q8.The probability that an ordinary or a non-leap year has 53 Sundays, is :

•  2/7
•  1/7
•  3/7
•  None of these

Solution
The probability that an ordinary or a non-leap year has 53 Sundays, is 1/7

Q9.Three letters are to be sent to different persons and addresses on the three envelopes are also written. Without looking at the addresses, the probability that the letters go into the right envelope is equal to:

•  1/27
•  1/9
•  4/27
•  1/6

Solution
The probability that the letters go into the right envelope is equal to 1/6

Q10. The probability of getting head and tail alternately in three throws of a coin (or a throw of three coins), is :

•  1/8
•  1/4
•  1/3
•  3/8

Solution
The probability of getting head and tail alternately in three throws of a coin (or a throw of three coins), is 1/4